Question

A block of mass m is conducted to a light spring of force constant k. The system is placed inside a damping medium of damping constant b. The instantaneous values of displacement, acceleration and energy of the block are x, a and E respectively. The initial amplitude of oscillation is A and ω' is the angular frequency of oscillations. The incorrect expression related to the damped oscillations is

• A. $\omega'=\sqrt{\frac{k}{m}-\frac{b^2}{4m^2}}$
• B. $E=\frac{1}{2}kA^2e^{-\frac{bt}{m}}$
• C. $m\frac{d^2x}{dt^2}+b\frac{dx}{dt}+kx=0$
• D. $x=Ae^{-\frac{b}{m}}\cos(\omega't+\phi)$

Answer 1

Answer: (D)

$x=Ae^{-\frac{b}{m}}\cos(\omega't+\phi)$

Answer 2

The correct answer is (D) : $x=Ae^{-\frac{b}{m}}\cos(\omega't+\phi)$